MCQ Questions for Class 8 Maths Squares And Square Roots Quiz 3

Pythagorean triplet, whose one member is

$16,$ is

$~16,~63,~65.$
State true or false.

0%
True
0%
False

Explanation

$2k,$

$(k^2 + 1)$ and

$(k^2 - 1)$ form a Pythagorean triplet for any number,

$k > 1$

Let

$2k = 16$
Hence,

$k = 8$

and,

$k^2 + 1 = 8^2 + 1= 64 + 1 = 65$
and,

$k^2 - 1 = 8^2 - 1 = 64 - 1 = 63$

Check the answers:

$63^2 + 16^2 = 3969 + 256 = 4225 = 65^2$

Hence, the triplet is

$16, 63,65$

The least number which is a perfect square and has

$540$ as a factor is

0%
$8,100$
0%
$6,400$
0%
$4,900$
0%
$3,600$

Explanation

The number must be a product of

$540$ and another number.

$540 = 9\times 4\times 15$
Now, the least number to be multiplied with

$540$ is

$15$ to make it a perfect square.
So, the required number is

$540\times 15 = 8100$

The Pythagorean triplet of number 18 is 18,80,82

State true or false.

0%
True
0%
False

Explanation

$2k$ ,

$(k^2 + 1)$ and

$(k^2 - 1)$ form a Pythagorean triplet for any number, k > 1

Let

$2k = 18$
Hence,

$k = 9$

and,

$k^2 + 1 = 9^2 + 1= 81 + 1 = 82$
and,

$k^2 - 1 = 9^2 - 1 = 81 - 1 = 80$

Check the answers:

$18^2 + 80^2 = 324 + 6400 = 6724 = 82^2$

Hence, the triplet is

$18, 80,82$

$16^{2}=256,$ then which of the following are perfect squares ?

0%
$\sqrt{0.00256}$
0%
$\sqrt{0.0256}$
0%
$\sqrt{3.69-1.13}$
0%
$\sqrt{12.8\div 5}$

Explanation

$\sqrt{0.0256}=0.16$

$\sqrt{3.69-1.14}=\sqrt{2.56}=1.6$

$\sqrt{12.8\div 5}=\sqrt{2.56}=1.6$

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

0%
16
0%
20
0%
25
0%
32

Explanation

Total number of children in a school =

$500$
For P.T. Drill number of rows = number of columns =

$x$
The number of children who will be left out =

$500 - x^2$ . The square root of

$500$ gives remainder as 16 that means, the square of

$22$ is less than

$500$ by

$16$
To make it a perfect square =

$500-16 = 484$
Therefore, number of children left will be

$16$

By splitting into prime factors, find the square root of

$729$ .

0%
$27$
0%
$21$
0%
$17$
0%
$87$

Explanation

Prime factorisation of

$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$

$\sqrt{729} = \sqrt{3 \times 3\times 3\times 3 \times 3\times 3} = 3 \times 3\times 3 = 27$

By splitting into prime factors, find the square root of

$11025$ .

0%
$1005$
0%
$105$
0%
$100$
0%
$115$

Explanation

Prime factorisation of $11025 = {5} ^{2} \times { 3 } ^ {2} \times { 7 } ^ {2}$
$\sqrt {11025} = \sqrt {{5} ^{2} \times { 3 } ^ {2} \times { 7 } ^ {2}} = 5 \times 3 \times 7= 105$ .

By splitting into prime factors, find the square root of

$5184$ .

0%
$72$
0%
$42$
0%
$52$
0%
$48$

Explanation

Prime factorisation of $5184$ can be obtained as,

$5184 =2\times2\times2\times2\times2\times2\times3\times3\times3\times3$

$= {2} ^{6} \times { 3 } ^ {4}$
$\therefore \sqrt {5184} = \sqrt {{2} ^{6} \times { 3 } ^ {4}} = {2} ^{3} \times { 3 } ^ {2} = 8 \times 9 = 72$

Find the smallest number by which 2592 be multiplied so that the product is a perfect square.

0%
2
0%
4
0%
5
0%
8

Explanation

$\textbf{Step-1: Find the prime factorization of given expression & ungrouped pair.}$

$\text{We have given 2592}$

$\therefore$

$\text{Prime factorization of}$

$2592 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$

$\text{Now,}$

$\text{On grouping the factors in pairs, we notice that one 2 is left out.}$

$\text{So, we should multiply 2592 with 2, so that prime factor 2 gets grouped in pairs.}$

$\textbf{Hence, 2592 should be multiplied by 2 to make it a perfect square.}$

$\textbf{Option - A}$

By splitting into prime factors, find the square root of

$396900$

0%
$630$
0%
$450$
0%
$520$
0%
$620$

Explanation

Prime factorisation of

$396900 = {2} ^{2} \times { 3 } ^ {4} \times { 5 } ^ {2} \times {7} ^ {2}$

$\sqrt {396900} = \sqrt {{2} ^{2} \times { 3 } ^ {4} \times { 5 } ^ {2} \times {7} ^ {2} } = 2 \times {3}^{2} \times 5 \times 7= 630$ .

Find the square root of

$324$ .

0%
$18$
0%
$16$
0%
$28$
0%
$24$

Explanation

The prime factorization of 324 is given as

$324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3$

$\sqrt{324} = \sqrt{\left(2\times2 \right) \times \left(3\times3 \right) \times \left(3\times 3\right)}= 2 \times 3 \times 3 = 18$

$\therefore \sqrt{324} = 18$ .

Find the smallest number by which 12748 be multiplied so that the product is a perfect square.

0%
3187
0%
7814
0%
4577
0%
1842

Explanation

$\textbf{Step -1: Factors of 12748.}$

$\text{By prime factorization method, we get, }$

$12748 = 2\times 2\times 3187$

$\textbf{Step -2: Finding the left out factor.}$

$3187 \text{ is a prime number and is not grouped with any other number.}$

$\text{Hence 12748 must be multiplied by 3187 so that the product is a perfect square.}$

$\textbf{Hence option A is correct.}$

The square root of

$245$ correct to two places of decimal is

$15.65.$

0%
True
0%
False

Explanation

Let us rewrite

$245$ as the product of its prime factors,

$\begin{aligned}{}245 &= 5 \times 7 \times 7\\ &= 5 \times {7^2}\\\sqrt {245}& = 7\sqrt 5 \\& = 7 \times 2.236\\ &= 15.652\\ &\approx 15.65\end{aligned}$

Hence, the given statement is true.

The square root of 82.6 correct to two places of decimal is 9.09
State true or false.

0%
True
0%
False

Explanation

$\quad \\ \quad \quad \quad \quad \quad 9.087\\ \quad \quad \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 9)82.60\quad 00\\ \quad \quad \quad -81\quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 180)\quad 01\quad 60\\ \quad \quad -0000\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 1808)\quad 160\quad 00\\ \quad \quad -\quad \quad 12864\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ 19167)\quad \quad \quad \quad \quad 3136\quad 00\quad \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad -31129\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \qquad \qquad \qquad \qquad 282471\quad$

Find the square root of

$4761$ .

0%
$69$
0%
$59$
0%
$49$
0%
$48$

Explanation

$\therefore \sqrt{4761} = 69$

or,

Since the sum of digits of the given number is 18, therefore it is divisible by 3.

$\Rightarrow 4761 = 3\times 1587 = 3\times 3\times 529 = 3\times 3\times 23\times 23 =$ square of

$23$

The square root of

$15129$ is

0%
$123$
0%
$223$
0%
$113$
0%
$213$

Explanation

$\therefore \sqrt{15129} = 123$

The square root of

$34969$ is:

0%
$177$
0%
$187$
0%
$197$
0%
$157$

Explanation

$\therefore \sqrt{34969} = 187$

$34969=11\times 11\times 17\times 17$

$\sqrt{34969}=\sqrt{11\times 11\times 17\times 17}$

$=11\times 17=187$

State true or false:

The square root of 56 correct to three decimal places is 7.483.

0%
True
0%
False

Explanation

Square root of 56 to three places of decimal is 7.483
Hence it is true so answer is

$1$

Find the least number that must be subtracted from

$23497$ so that the resulting number is a perfect square.

0%
84
0%
48
0%
88
0%
15

Explanation

Taking the root of the given number

$23497$ , we find that

$88$ has been left as shown below:

Hence,

$88$ is the least number that must be subtracted so that the resulting number is a perfect square.

Find the square root of

$\displaystyle 6 \frac{7}{8}$ correct to two decimal places

0%
$2.62$
0%
$2.61$
0%
$2.63$
0%
$2.6$

Explanation

$\displaystyle 6 \frac{7}{8}$

$=\dfrac{55}{8}$

$=6.875$


$2$ $2$	$6.875$ $4$
$46$ $6$	$287$ $276$
$522$	$1150$ $1044$
	$6$

Therefore,
Square root of

$\displaystyle 6 \frac{7}{8}=2.62$

The square root of 0.065 correct to three places of decimal is 0.255
State true or false

0%
True
0%
False

Explanation

$\quad \\ \quad \quad \quad \quad \quad 0.254\\ \quad \quad \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 2)\quad 0.06\quad 50\quad 00\\ \quad \quad \quad -0.04\quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 45)\quad \quad \quad 2\quad 50\\ \quad \quad -\quad \quad 225\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 504)\quad \quad \quad 25\quad 00\\ \quad \quad -\quad \quad \quad \quad 2016\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \quad \quad \quad \quad \quad \quad \quad \quad 484\quad \quad \quad \\ \\$

State true or false:

The square root of 5.2005 correct to two decimal places is 2.28.

0%
True
0%
False

Explanation

$\quad \\ \quad \quad \quad \quad \quad 2.287\\ \quad \quad \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 2)5.\quad 20\quad 05\\ \quad \quad \quad -4\quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 42)01\quad 20\\ \quad \quad -0084\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 448)\quad 036\quad 05\\ \quad \quad -\quad \quad 3584\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad \quad \quad \quad \quad \quad 21\quad$

Squares of which of the following numbers will have 1(one) at their unit's place :

0%
57
0%
81
0%
139
0%
73
0%
64
0%
831

State true or false:

The square root of 0.008 correct to three decimal places is 0.089.

0%
True
0%
False

Explanation

$\quad \\ \quad \quad \quad \quad \quad 0.089\\ \quad \quad \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 0)\quad 0.00\quad 80\quad 00\\ \quad \quad \quad -0.00\quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 8)\quad \quad 00\quad 80\\ \quad \quad -\quad 0064\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 169)\quad \quad \quad 16\quad 00\\ \quad \quad -\quad \quad \quad \quad 1529\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \quad \quad \quad \quad \quad \quad \quad \quad 71\quad \quad \quad \\ Rounding\quad off\quad :\quad 0.089\\ \\$

Find the square root of

$\displaystyle 1 \frac{5}{16}$ correct to two decimal places

0%
$1.14$
0%
$1.15$
0%
$1.65$
0%
$1.12$

Explanation

$\displaystyle 1 \dfrac{15}{16}$

$=\dfrac{21}{16}$

$=1.3125$


$1$ $1$	$1.3125$ $1$
$21$ $1$	$31$ $21$
$224$ $4$	$1025$ $896$
$2285$	$12900$ $11425$ $1475$

Therefore,
Square root of

$\displaystyle 1 \frac{15}{16}=1.145$

$=1.15$

Seeing the value of the digit at unit's place, state which of the following can be square of a number :

0%
$3051$
0%
$2332$
0%
$5684$
0%
$6908$
0%
$50699$
0%
$920546$

Explanation

The square of the numbers must end with any of the digits

$0$ ,

$1$ ,

$4$ ,

$5$ ,

$6$ or

$9$ .
Example:-

${ 1 }^{ 2 }\quad =\quad 1$

${ 12 }^{ 2 }\quad =\quad 144$

${ 13 }^{ 2 }\quad =\quad 139$

${ 5 }^{ 2 }\quad =\quad 25$
Also, a perfect square has even number of zeros at the end. Example :-

$100, 400, 640000$ .
(A)Here, the number is

$3051$ .
The unit's digit is

$1$ . Thus, It can be a perfect square.
(B)Here, the number is

$2332$ .
The unit's digit is

$2$ . Thus, It cannot be a perfect square.
(C)Here, the number is

$5684$ .
The unit's digit is

$4$ . Thus, It can be a perfect square.
(D)Here, the number is

$56908$ .
The unit's digit is

$8$ . Thus, It cannot be a perfect square.
(E)Here, the number is

$50699$ .
The unit's digit is

$9$ . Thus, It can be a perfect square.
(F)Here, the number is

$920546$ .
The unit's digit is

$6$ . Thus, It can be a perfect square.

State true or false.
The square root of 0.602 correct to two decimal places is 0.78.

0%
True
0%
False

Explanation

$\quad \\ \quad \quad \quad \quad \quad 0.77\\ \quad \quad \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 7)\quad 0.60\quad 20\\ \quad \quad \quad -0.49\quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ 147)\quad \quad 11\quad 20\\ \quad \quad -\quad 1029\quad \quad \downarrow \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad \quad \quad \quad 191\quad$

If the square ends with

$5,$ then the number has ___ at the units place.

0%
$7$
0%
$6$
0%
$5$
0%
$1$

Explanation

For example,

$5 \times 5 = 25$

$25 \times 25 = 625$ ( square ends with

$5$ )

Thus if square ends with

$5$ then the number has to be

$5$ at the units place.
Therefore, C is the correct answer.

Which of the following numbers will not have 6 at the unit's place in their squares?

0%
35
0%
23
0%
64
0%
76
0%
94
0%
42
0%
98

Explanation

We know that when the unit place of a number is

$4$ or

$6$ then the square of that number has a unit place equal to

$6$ .

(A) Unit place of

$(35)^2$ = Unit place of

$5^2$ = 5
(B) Unit place of

$(23)^2$ = Unit place of

$3^2$ = 9
(C) Unit place of

$(64)^2$ = Unit place of

$4^2$ = 6
(D) Unit place of

$(76)^2$ = Unit place of

$6^2$ = 6
(E) Unit place of

$(94)^2$ = Unit place of

$4^2$ = 6
(F) Unit place of

$(42)^2$ = Unit place of

$2^2$ = 4
(G) Unit place of

$(98)^2$ = Unit place of

$8^2$ = 4

Hence, A, B, F, G are the correct answers.

Consider the Following values of the three given number

$\displaystyle \sqrt{103},$

$\displaystyle \sqrt{99.35},$

$\displaystyle \sqrt{102.20},$
1.10.1489 (approx,)
2.10.109(approx,)
3.9.967 (approx,)
The correct sequence of the these values matching with the above number is:

0%
1, 2, 3
0%
1, 3, 2
0%
2, 3, 1
0%
3, 1, 2

Explanation

$\sqrt{3}=10.14889$

$\sqrt{99.35}=9.967$

$\sqrt{102.30}=10.1094$
Hence,The correct sequence of the these values matching with the above number is:1,3,2

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 3 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 3 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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